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The value problem in stochastic games

Abstract : Game theory proved to be very useful in the field of verification of open reactive systems. This is due to the wide variety of games' model that differ in the way players interact and the amount of information players have. In this thesis, we study the value problem for games where players have full knowledge on their current configuration of the game, partial knowledge, and no knowledge. In the case where players have perfect information, we study the value problem for objectives that consist in combination of qualitative and quantitative conditions. In the case of one player stochastic games, we show that the values are computable in polynomial time and show that the optimal strategies exist and can be implemented with finite memory. We also showed that our construction for parity and positive-average Markov decision processes extends to the case of two-player stochastic games. In the case where the players have partial information, we study the value problem for reachability objectives. We show that computing the set of states with value 1 is an undecidable problem and introduce a decidable subclass for the value 1 problem. This sub class is PSPACE-complete in the case of blind controllers and EXPTIME is the setting of games with partial observations.
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Contributor : Youssouf Oualhadj <>
Submitted on : Tuesday, December 18, 2012 - 2:38:56 PM
Last modification on : Thursday, January 11, 2018 - 6:20:17 AM
Long-term archiving on: : Sunday, December 18, 2016 - 4:44:58 AM

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  • HAL Id : tel-00766347, version 2

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Youssouf Oualhadj. The value problem in stochastic games. Computer Science and Game Theory [cs.GT]. Université Sciences et Technologies - Bordeaux I, 2012. English. ⟨tel-00766347v2⟩

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